Worksheet: Dividing Polynomials by a Divisor of First Degree with No Remainder

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In this worksheet, we will practice dividing polynomials using an algorithm similar to that of long division of integers with no remainder.

Q1:

Knowing that the length of a rectangle is 𝑥 + 5 and its area is 2 𝑥 + 9 𝑥 − 5 2 , express the width of the rectangle algebraically.

  • A 𝑥 − 1
  • B 2 𝑥 + 1
  • C 𝑥 + 1
  • D 2 𝑥 − 1
  • E 2 𝑥 − 2

Q2:

Knowing that the length of a rectangle is 3 𝑥 − 4 and its area is 6 𝑥 − 8 𝑥 + 9 𝑥 − 9 𝑥 − 4 4 3 2 , express the width of the rectangle as a polynomial in standard form.

  • A 2 𝑥 + 3 𝑥 − 1 3
  • B 3 𝑥 + 2 𝑥 + 1 3
  • C 3 𝑥 + 2 𝑥 − 1 3
  • D 2 𝑥 + 3 𝑥 + 1 3
  • E 𝑥 + 3 𝑥 + 2 3

Q3:

Find the value of 𝑎 given that 6 𝑥 + 𝑎 𝑥 − 3 0 𝑥 − 2 1 𝑥 + 1 0 4 3 2 is divisible by ( 2 𝑥 + 5 ) .

Q4:

The expression 4 𝑦 + 8 𝑦 − 5 2 has two factors. One factor is ( 2 𝑦 + 5 ) , what is the other factor?

  • A ( 3 𝑦 − 1 )
  • B ( 2 𝑦 + 1 )
  • C ( 2 𝑦 + 2 )
  • D ( 2 𝑦 − 1 )
  • E ( 2 𝑦 − 2 )

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